A mathematical analysis of the myogenic hypothesis with special reference to autoregulation of renal blood flow

To test the hypothesis that autoregulation of renal blood flow could result from myogenic regulation of arterial/arteriolar wall tension, we have explored a model based on the assumptions that (1) each preglomerular vessel segment reacts to a change in transmural pressure by altering its internal radius until the initial change in wall tension is reduced by a gain factor, (2) postglomerular structural resistance remains unchanged, (3) extravascular tissue pressure equals intrarenal venous pressure, and (4) the renal vascular system can be represented by one unbranched tube. General equations were obtained for flow and segmental radii and pressure as functions of aortic pressure. With a gain factor of 1 and a glomerular capillary pressure of 50% of aortic pressure under control conditions, the model predictions agree well with experimental data in dogs. Increasing aortic pressure from about 60% of control level causes only slight increase of blood flow. A rise in tissue pressure up to 40% of aortic pressure causes only moderate reduction. Changes in vessel radii begin in proximal vessel segments and spread distally toward glomerulus at increasing changes in aortic and tissue pressures from their control levels. Glomerular capillary pressure is autoregulated in proportion to blood flow. The degree of autoregulation is only moderately dependent on the gain factor: A moderate impairment caused by reducing the gain factor from 1 to 0.7 may be compensated by locating the myogenically responsive wall layer a distance 0.2 times the internal radius from the vessel lumen. "Superautoregulation," i.e., a rise in flow at reduced aortic pressure, is not possible. An upper limit of autoregulation is obtained only with the additional assumption of a fall in contractile force at extreme shortening of the muscle fibers. No definitive biological proof has yet been provided for a segmental wall tension-regulating mechanism in the preglomerular vessels, and obviously its existence cannot be proved by a mathematical model. However, if such a mechanism does exist, it can explain most of the renal resistance changes at varying arterial and intrarenal pressures, as well as the observed autoregulation of terminal interlobular arterial pressure.